Question

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

A rhombus is shown. Lines are drawn from each point to the opposite point to form 4 right triangles. The other 2 angle measures are 30 and 60 degrees. The base length of each triangle is 15 feet.


What is the distance around the perimeter of the garden?


60 ft

60 StartRoot 3 EndRoot ft

120 ft

120 StartRoot 3 EndRoot ft

Answer 1

C

Explanation:

Answer 2

c) 120 ft

Explanation:

Let's consider the rhombus has 4 sides, A, B, C, and D.

To find the length of each side, let's first find the length AE.

From the diagram, AE is half of AC and AC = 30 ft.

Therefore,

AE = ½ * 30

AE = 15 ft

Let's find the length AD, since we are looking for the distance around the perimeter.

`AD = (15)/(sin30) = (15)/(0.5) = 30 ft`

We are told the rhombus is formed by four identical triangles.

Therefore the distance around the perimeter would be: AD+AD+AD+AD=

30 ft + 30 ft + 30 ft + 30 ft

= 120 ft

The distance around the perimeter of the garden is 120 ft